The hydrodynamics of single- and multi-particle fluidized beds: Steady and time-dependent flow regimes

A mathematical framework for modeling the steady state and dynamic behavior of multi-particle fluidized beds was developed using a continuum approach. Constitutive relations were adopted for closing the multi-phase equations using an excluded volume approach. The hydrodynamics of various fluidized beds of binary particles (having different diameters and densities) was examined, and steady state solutions were found for a system of (small & heavy) glass beads and (large & light) carbon char in water. Solutions characterize the composition and expansion behavior of mixing states, and provide a description of the observed phenomenon of “layer inversion”. Comparison with experimental data suggested that the hydrodynamic mechanism of fluid-particle interaction is not fully captured with an excluded volume assumption. Thus, we showed how experimental data can be used to derive functional forms for expressing complex hydrodynamic behavior within the framework of the model. Steady state results suggest that fluidized particles might exhibit different patterns of behavior if the direction of fluid flow was reversed. We thus examined the stability of single-component systems, operating in inverse and normal mode, and computed one-dimensional traveling wave solutions. Beds having reciprocal fluid to solid density ratios δ were compared to investigate how δ and the dimensionless Froude (Fr) number affect stability behavior and bifurcation structure. The Fr number appeared to be a good indicator of the strength of primary instabilities, and δ appeared to control the onset of the instability. High amplitude, one-dimensional traveling wave solutions exhibited reversed asymmetry of wave structure, and vertically traveling waves always propagated in the direction of fluid flow. The hydrodynamic stability of binary mixtures was examined to determine if mixtures are inherently more stable than their segregated counterparts. In a linear stability analysis, mixed beds of glass and carbon were always more stable than a (single-component) bed of glass, and always less stable than a (single-component) bed of carbon. Moreover, an increase in fluid velocity corresponded to an increase in carbon content in the mixture, resulting in a more stable mixture. These results suggest that the presence of the larger & lighter species serves to stabilize the mixed bed.